In the oil exploration industry, seismic data is obtained to enable scientists and engineers to develop a picture of underlying rock formations. The reflection seismic method attempts to image the top few kilometers of the earth's crust by artificially creating a wavefield at the earth's surface and then recording this wavefield at multiple locations as it returns to the surface mainly via reflections within the rock of the earth's crust. These wavefields are then processed in order to obtain images of the subsurface that can be used to help locate hydrocarbons.
As illustrated in FIG. 1, a wavefield is created at the surface at a source location, S, by setting off a percussive shock wave or shot that imparts wave energy into the ground. The shot is typically dynamite or a mechanical vibration system, such as a Vibroseis truck, that creates a sinusoidal signal of changing frequency through shaking the earth. The energy source approximates a point source.
A series of receivers or geophones at receiver points, R, set up as either a linear array (termed 2D seismic) or a two-dimensional array (3D seismic) around S, record the amplitude of wave energy that is received at each receiver point from reflections of the shot energy off underlying formations as a function of time, thus creating an array of time/amplitude data for each geophone location. In FIG. 1, schematically illustrating 3-D seismic, a two-dimensional array of receiver points ((1,1), (1,2), (1,3) . . . ) is shown around the shot, S with representative wave paths that might be received at (1,1) based on reflections off the underlying formations. The recording of the wavefield is not continuous but rather is sampled at discrete time intervals (typically 2 ms intervals) and space intervals, which is determined by the separation distance between geophones (typically 50 meters).
Reflections occur when the wavefield encounters a change in acoustic impedance, usually found at the boundaries between different rock types. Through various mathematical and statistical imaging techniques, an image of the sub-surface formations can be determined at varying levels of resolution. As shown schematically in FIG. 1A, a number of traces with a certain density of spatial distribution can be used to develop a picture of the depth and shape of an underlying discontinuity. However, as can be seen from FIG. 1A, no data exists for location A.
From an imaging perspective, it is preferred that the wavefield sampling is intense both in terms of time (ie smaller sampling interval) and space (higher density of shots and geophones). In practice, however, the sampling is usually more than required in time, t, and less than required in space (x,y). In addition, azimuthal sampling is usually less than adequate (that is source to receiver azimuths tend to be similar rather than evenly distributed over 360 degrees) and the distribution of offsets (source to receiver distance) is unbalanced and inadequate.
In general, therefore, the relative density of the shot and/or receiver points in a given area will enable the creation of images with relatively higher or lower resolution. However, as the cost of obtaining an ideally sampled dataset would be prohibitively expensive, the collection of seismic data must always be a balance between acceptable resolution and the cost of obtaining data with an acceptable resolution. Moreover, the collection of seismic data is often affected by other limitations including the specific surface geography of an area where because of specific natural geographical features such as lakes or steep terrain, man-made features, such as roads or buildings, or environmental restrictions, such as wildlife sanctuaries, the placement of shots and geophones in particular areas is prevented, thus leading to incomplete images or images with decreased resolution in particular areas.
Accordingly, as the cost of signal processing is relatively inexpensive compared to the cost of field data acquisition, there continues to be a need to improve the resolution of the images obtained from seismic data using the industry acceptable densities of geophone arrays. In addition, there is a need for systems that enable the interpolation of data into areas where a lack of shots and/or geophones have resulted in a lack of data.
Other Problems with Inadequately Sampled Data
Still further, a common manifestation of inadequate sampling is a low signal-to-noise ratio in the final image. Noise is a direct hindrance to the successful interpretation of seismic data, and great efforts are made to reduce noise. One very successful way to eliminate random or quasi-random noise is to record redundant data. Using this method, all raypaths that reflect from a common point in the subsurface are added together or stacked to create a stacked trace of high fold. As the desired reflection energy adds constructively from each trace, and the random noise does not, the random noise is cancelled out. As a result, the higher the fold, the higher the signal-to-noise ratio.
As noted above, in order to correctly image a geological structure in the subsurface, the surface spatial sampling must be adequate. Sampling theory describes or explains that the steeper an underlying structure is, the tighter the spatial sampling on the surface must be in order to correctly image it. If the spatial sampling is inadequate (ie geophones are too far apart), then spatial aliasing will result giving incorrect images.
Similarly, imaging complex structures may also require adequate sampling from a variety of azimuths to ensure that a variety of raypaths as defined by source-to-receiver raypaths provide sufficient data to avoid the reflection problems realized by complex structures that would otherwise result in a distorted or incomplete image.
Further still, the reflection amplitude and phase are not constant at all angles of reflection where both reflection amplitude and phase will vary with the angle of incidence of the raypath. These variations provide important information about the rock layers at an interface. In addition, various forms of unwanted coherent noise (as opposed to random noise) travel at velocities that differ from the primary (and desired) reflection energy. This difference in recorded arrival times becomes larger with increasing distance traveled (as defined by source-to-receiver offset) and thus can be used to effectively remove the unwanted coherent signal. However, in order to do this, a good balance of source-to-receiver offsets must be present at all points in the recorded dataset.
Further still, various processing steps rely on good statistics throughout the dataset. A less than adequate dataset from the field can limit the quality of the image processing. Steps that are hampered by inadequate sampling include derivation of refraction statics, deconvolution, operator design, reflection statics determination, velocity analysis, various noise attenuation techniques, pre- and post-stack migration and all reservoir analysis techniques, such as AVO/LMR analysis that use the variation of reflection amplitude with offset as their input. Shortcomings introduced by inadequate statistics in any of these steps can seriously impact the final image integrity.
As a result, there is a need for a system that continues to address the problems identified above with respect to the collection and interpretation of seismic data. In particular, there has been a need for a system that conveniently and effectively enables the interpolation of seismic data to provide an accurate or improved resolution of underlying formations around which there may be a shortage of data.